The Algebra & Geometry of Modern Physics

A little of history; complements of algebra; definition of Spin groups: algebra vs topology; two periodicities of properties of Clifford algebras; complex conjugation and antiparticles; the Chevalley theorem and the Brauer-Wall group: spinorial clock; Radon-Hurwitz numbers and vector fields on spheres; spinors on manifolds: two approaches; (S)pin structures; tensor bundles are natural; spinor bundles are not; triviality of spinor bundles of spheres; covariant differentiation of spinor fields; Dirac operator: Schroedinger's formula, spectrum on spheres.